The Big Idea
Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
**Problem 2.1:
Comparing Leisure Activities
a. Why don’t the numbers in the column add to the given total?
ans. The numbers don’t add to the given totals because one person can choose more than one activity.
b. Write three statements that use percents make comparison about the numbers of male and female participants in the various activities. Explain how you found the percents.
ans. Three statements that use percents to make comparison about the number of female and male participants in various activities are:
1. 21% of the males in total go bicycle riding, while only 19% of females go bicycle riding.
2. Only 16% of the females go camping, but 20% of the males go camping
3. While only 18% of the males exercise walk, 36% of the females exercise walk.
c. Write three statements that use percents to make comparisons about the numbers of teenage and older-adult participants in the various activities.
ans. Three statements that use percents to make comparisons about the number of teenage and older-adult participants in the various activities are:
1. While 41% of the people in the age group of 12-17 go bicycle riding, only 9% of the people from the age group of 55-64 go bicycle riding
2. 51% of the people in the age group of 12-17 go swimming, but only 13% of the people in the age group of 55-64 go swimming.
3. Only 13% of the people in the age group of 12-17 exercise walk, but 37% of the people in the age group of 55-64 exercise walk
d. Write three statements that make comparisons about the data without using percents.
ans. Three statements that make comparison with using percents are:
1. Males prefer bicycle riding to females, by a ratio of 24,562,000 to 23,357,000.
2. People from the age group of 12-17 outnumber those in the age group of 55-64, in fishing by 2,981,000.
3. Males who prefer swimming outnumber those whop prefer it, in the age group of 55-64 by 24,956,000
Problem 2.1 follow up:
1. Explain how you might decide when percents would be a good way to make comparison and when other forms of comparison would be better.
ans. Percent would be a good way to compare when we are comparing a number with a 100. Ratios would be a good way to compare when using measurements and units. Fractions would be a good way to compare when we are comparing to numbers.
2. Can you compare the participation of teenage boys in these activities to participation of older-adult women by using data in the table? Explain.**
ans. No, we cannot compare the teenage boys to the older-adult women. This is because the data in the table does not tell us how many teenage boys or older-adult women participate in these activities.
9.11.09
A.B
The Big Idea
Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.
**Problem 2.1:
Comparing Leisure Activities
a. Why don’t the numbers in the column add to the given total?
ans. The numbers don’t add to the given totals because one person can choose more than one activity.
b. Write three statements that use percents make comparison about the numbers of male and female participants in the various activities. Explain how you found the percents.
ans. Three statements that use percents to make comparison about the number of female and male participants in various activities are:
1. 21% of the males in total go bicycle riding, while only 19% of females go bicycle riding.
2. Only 16% of the females go camping, but 20% of the males go camping
3. While only 18% of the males exercise walk, 36% of the females exercise walk.
c. Write three statements that use percents to make comparisons about the numbers of teenage and older-adult participants in the various activities.
ans. Three statements that use percents to make comparisons about the number of teenage and older-adult participants in the various activities are:
1. While 41% of the people in the age group of 12-17 go bicycle riding, only 9% of the people from the age group of 55-64 go bicycle riding
2. 51% of the people in the age group of 12-17 go swimming, but only 13% of the people in the age group of 55-64 go swimming.
3. Only 13% of the people in the age group of 12-17 exercise walk, but 37% of the people in the age group of 55-64 exercise walk
d. Write three statements that make comparisons about the data without using percents.
ans. Three statements that make comparison with using percents are:
1. Males prefer bicycle riding to females, by a ratio of 24,562,000 to 23,357,000.
2. People from the age group of 12-17 outnumber those in the age group of 55-64, in fishing by 2,981,000.
3. Males who prefer swimming outnumber those whop prefer it, in the age group of 55-64 by 24,956,000
Problem 2.1 follow up:
1. Explain how you might decide when percents would be a good way to make comparison and when other forms of comparison would be better.
ans. Percent would be a good way to compare when we are comparing a number with a 100. Ratios would be a good way to compare when using measurements and units. Fractions would be a good way to compare when we are comparing to numbers.
2. Can you compare the participation of teenage boys in these activities to participation of older-adult women by using data in the table? Explain.**
ans. No, we cannot compare the teenage boys to the older-adult women. This is because the data in the table does not tell us how many teenage boys or older-adult women participate in these activities.